The present invention generally relates to a lithography process. More specifically, the present invention relates to a lithography method having a simulation method with a Diffused Aerial Image Model (“DAIM”).
A simulation technology of an optical lithography process is extremely excellent in the optimization of a cell layout, prediction of optimum conditions of a complicated process or prompt processing of huge data. Thus, the simulation technology has been widely used to reduce trials and errors in unit process development and new device development to shorten a development period.
Generally, a simulation tool of a photoresist process in the lithography process comprises: 1) a tool such as SOLID-C and Prolith, which simulates the whole process including composition, exposure and baking of photoresist materials; and 2) a tool such as a simulation function in OPC, which quantifies an aerial image to obtain an approximate result. Although the first tool has more accurate calculation results than the second tool, it takes a long time and is complicated. Otherwise, the second tool is less accurate than the first tool although the second tool's calculating speed is fast. Specifically, the second tool to optimize a mask layout requires an Optical Proximity effect Correction (“OPC”). A widely used method for OPC provides considering an aerial image intensity contour as a top view of the photoresist film pattern to approximate a target layout desired by the aerial image.
Meanwhile, a chemical amplification photoresist generates an acid by a Photo Active Generator (“PAG”) due to photon energy in an exposure process. When the standard concentration of the PAG is called “P” and the light intensity is called “I”, the concentration change resulting from resolution of the PAG for an exposure time t satisfies ∂P(x,y,t)/∂t=−C(x,y)P(x,y,t). Here, C as a proportional constant is the same as Dill's C. The acid is generated as much as the amount of the resolved PAG. Provided that the sum total of concentrations of the PAG and the acid is constant at all times, the standard concentration distribution A0 of the acid right after exposure is represented by A0(x,y)=1−e−CE(x,y). If the exponent value of the exponential function is not large, the above equation A0 approximately represents A0(x,y)≅CE(x,y). As a result, the distribution of the acid is proportional to that of the intensity of the exposed light. The acid generated by the exposure process is diffused by thermal energy during a subsequent post exposure baking (“PEB”) process. During the PEB process, the concentration A of the standard acid satisfies ∂A(x,y,t′)/∂t′=−D∇2A(x,y,t′) in accordance with the Fick's law, where t′ represents a PEB time. The solution of the above differential equation as well known expresses A(x,y,t′)=F−1e−σ2(ξ2+η2)/2F(A0(x′,y′)) if (ξ, η) are used as conjugation coordinates with respect to (x, y) coordinates in Fourier transformation.
During the PEB process, while the acid is diffused, it attacks a chain ring of a dissolution inhibitor or a protection group in a photoresist film. As a result, the acid is separated from a base polymer so that it may be dissolved in a developing solution. Since the concentration of the polymer separated from each spatial coordinate depends on the distribution of the average acid with respect to time in each point for the PEB time tB, the concentration M(x, y) of the separated polymer is represented as follows:
            M      ⁡              (                  x          ,          y          ,                      t            B                          )              ≈                  A        ⁡                  (                      x            ,            y            ,            t                    )                    _        ⁢          ⁢          =                              ∫          0                      t            B                          ⁢                              A            ⁡                          (                              x                ,                y                ,                t                            )                                ⁢                      ⅆ            t                                      t        B              ⁢                  ⁢                  =                  2                  σ          B          2                    ⁢                                    F                          -              1                                ⁡                      [                                                            1                  -                                      ⅇ                                                                  -                                                                              σ                            B                            2                                                    ⁡                                                      (                                                                                          ξ                                2                                                            +                                                              η                                2                                                                                      )                                                                                              /                      2                                                                                                            ξ                    2                                    +                                      η                    2                                                              ⁢                              F                ⁡                                  (                                                            A                      0                                        ⁡                                          (                                                                        x                          ′                                                ,                                                  y                          ′                                                                    )                                                        )                                                      ]                          .            
The above-described method is very effective in simulation of the lithography process. As the pattern becomes smaller and the Rayleigh k1 constant, which shows a degree of process complexity, is decreased, the above-described method is however inconsistent with actual experimental results.
FIG. 1 is a photograph illustrating an actual pattern of a lithography process. Images of FIGS. 2a and 2b obtained by a conventional simulation method are different from the actual pattern of FIG. 1. In other words, the connected image in the dotted circle of FIGS. 2a and 2b is different from the simulation result in the actual disconnected pattern. FIG. 2a shows when the diffusion constant is 0 while FIG. 2b shows when the diffusion constant is 0.375.
In the above-described conventional simulation method of the lithography process, simulation errors are generated as the process becomes more difficult. Accordingly, the simulation results are not reliable.